jzoj6002

题意

做法

令\(N=\lfloor\frac{n-1}{2}\rfloor\)：\(ans=\sum\limits_{i=1}^{N}\sum\limits_{j=2 i+1}^n(y-2)!{j-2\choose y-2}(n-y)!=(y-2)!(n-y)!\sum\limits_{i=1}^{N}({n-1\choose y-1}-{2i-1\choose y-1})\)

令\(A_{y-1}={1\choose y-1}+{3\choose y-1}+...+{2N-1\choose y-1}，B={2\choose y-1}+{4\choose y-1}+...+{2N\choose y-1}\)

有\(A_{y-1}+B_{y-1}={2N+1\choose y}\)，\(A_{y-1}+A_{y-2}=B_{y-1}\)，则：

\[A_{y-1}=\frac{{2lim+1\choose y}-A_{y-2}}{2} \]

则\(A\)可以\(O(n)\)递推出来，预处理即可